Hello, Pls see attached. ty,

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Pls see attached.

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### Nutritional Content Analysis using F-Test

#### Experimental Setup:

Emily is conducting an experiment to check if different nutritional formulas have varying effects on mice. Specifically, she uses 5 mice to test each type of formula. The net weight gain in grams for each mouse after a specified time period is recorded as follows:

| Formula C | Formula B |
|-----------|-----------|
| 51        | 47        |
| 41        | 38        |
| 38        | 49        |
| 46        | 46        |
| 49        | 44        |

#### Statistical Analysis:

An F-Test Two-Sample for Variances is conducted to compare the variances of the weight gains for the two formulas.

**Variables:**
- **Variable 1** corresponds to Formula C.
- **Variable 2** corresponds to Formula B.

**Summary of Statistical Data:**

| Statistic               | Variable 1          | Variable 2  |
|-------------------------|---------------------|-------------|
| **Mean**                | 45                  | 44.8        |
| **Variance**            | 29.5                | 17.7        |
| **Observations**        | 5                   | 5           |
| **Degrees of Freedom (df)** | 4               | 4           |

**F-Test Results:**

| Result                  | Value                        |
|-------------------------|------------------------------|
| **F**                   | 1.666666667                  |
| **P(F <= f) one-tail**  | 0.31640625                   |
| **F Critical one-tail** | 6.388232909                  |

**Key Questions:**

1. **The Critical F-Value** for this problem needs to be rounded to three decimal places:

   **F Critical one-tail** is rounded to **6.388**.

2. **Decision Making:**
   
   We need to determine whether we have enough evidence to conclude that the variances of weight gains being compared are different. 
   
   Based on the F-Test results, do we have enough evidence?

   **TRUE OR FALSE?**.
Transcribed Image Text:### Nutritional Content Analysis using F-Test #### Experimental Setup: Emily is conducting an experiment to check if different nutritional formulas have varying effects on mice. Specifically, she uses 5 mice to test each type of formula. The net weight gain in grams for each mouse after a specified time period is recorded as follows: | Formula C | Formula B | |-----------|-----------| | 51 | 47 | | 41 | 38 | | 38 | 49 | | 46 | 46 | | 49 | 44 | #### Statistical Analysis: An F-Test Two-Sample for Variances is conducted to compare the variances of the weight gains for the two formulas. **Variables:** - **Variable 1** corresponds to Formula C. - **Variable 2** corresponds to Formula B. **Summary of Statistical Data:** | Statistic | Variable 1 | Variable 2 | |-------------------------|---------------------|-------------| | **Mean** | 45 | 44.8 | | **Variance** | 29.5 | 17.7 | | **Observations** | 5 | 5 | | **Degrees of Freedom (df)** | 4 | 4 | **F-Test Results:** | Result | Value | |-------------------------|------------------------------| | **F** | 1.666666667 | | **P(F <= f) one-tail** | 0.31640625 | | **F Critical one-tail** | 6.388232909 | **Key Questions:** 1. **The Critical F-Value** for this problem needs to be rounded to three decimal places: **F Critical one-tail** is rounded to **6.388**. 2. **Decision Making:** We need to determine whether we have enough evidence to conclude that the variances of weight gains being compared are different. Based on the F-Test results, do we have enough evidence? **TRUE OR FALSE?**.
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